Lattice Boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media

A new algorithm for imposing the contact angle on solid surfaces is proposed in the Lattice Boltzmann color-gradient model. The capability and accuracy of this algorithm are validated by simulation of contact angles for a droplet resting on a flat surface and on a cylindrical surface. The color-gradient model with the proposed contact angle algorithm is then used to study the capillary valve effect in porous media. As a preliminary study, the capillary valve effect is explained by simulating immiscible two-phase displacement within a single-pore geometry. It is shown that the capillary valve effect is accurately captured by the present simulations. Further simulations of drainage and imbibition are also conducted to understand the capillary valve effect in an experiment-matched pore-network micromodel. The simulated results are found to agree quantitatively with the experimental results reported in literature, except for a few differences which result from the exclusion of contact angle hysteresis in the proposed algorithm.